Quadcopter unmanned aerial vehicles (UAVs) have gained widespread adoption in both civilian and military applications across China due to their compact structure, vertical takeoff and landing capabilities, and operational flexibility. However, small quadcopter UAVs, commonly used in logistics, surveillance, and agricultural monitoring, often suffer from insufficient flight power and limited structural expansion. The rotor diameter of such vehicles is typically constrained between 0.1 m and 0.2 m, and the flight speed ranges from 5 to 15 m/s, corresponding to a Reynolds number of $10^4$ to $10^5$. Under these low-Reynolds-number conditions, optimizing the blade airfoil becomes a crucial approach to enhance the overall aerodynamic performance without altering the propeller diameter. In this study, I focus on the widely used CLARK Y airfoil for small quadcopter China UAV rotors and perform an optimization using a genetic algorithm combined with the Hicks-Henne shape function and CFD validation.
1. Airfoil Parameterization Using the Hicks-Henne Method
To represent the airfoil geometry with a limited number of design variables, I employed the improved Hicks-Henne shape function method. The airfoil contour is defined by the superposition of a baseline airfoil and a series of bump functions. The general expression for the airfoil shape is given by:
$$
y(x) = y_0(x) + \sum_{k=1}^{N} c_k f_k(x)
$$
where $y_0(x)$ is the baseline airfoil (CLARK Y), $N$ is the number of shape functions, $c_k$ are the design parameters to be optimized, and $f_k(x)$ are the Hicks-Henne bump functions defined as:
$$
f_1(x) = x^{0.25}(1-x)e^{-20x}, \quad k=1
$$
$$
f_k(x) = \sin^3\!\bigl(\pi x^{e(k)}\bigr), \quad k \geq 2
$$
with $e(k) = \log(0.5)/\log(x_k)$ and $x_k$ chosen as 0.15, 0.3, 0.45, 0.6, 0.75, 0.9 for $k=2,\ldots,7$. To improve the trailing‑edge flexibility, I added a trailing‑edge perturbation function for $k = N$:
$$
f_N(x) = \alpha x(1-x)e^{-\beta(1-x)}
$$
with $\alpha = 5$ and $\beta = 10$. The upper and lower surfaces are parameterized separately, each using five design variables (total 10 variables). The constraints for these variables are listed in Table 1.
| Upper surface parameter | Constraint | Lower surface parameter | Constraint |
|---|---|---|---|
| $c_1$ | [-0.08, 0.06] | $c_6$ | [-0.08, 0.06] |
| $c_2$ | [-0.07, 0.07] | $c_7$ | [-0.05, 0.09] |
| $c_3$ | [-0.09, 0.05] | $c_8$ | [-0.07, 0.09] |
| $c_4$ | [-0.04, 0.01] | $c_9$ | [-0.08, 0.06] |
| $c_5$ | [-0.05, 0.09] | $c_{10}$ | [-0.06, 0.08] |
2. Optimization Algorithm and Objectives
Since the lift coefficient $C_L$ and lift-to-drag ratio $C_L/C_D$ are positively correlated within the low angle‑of‑attack range (below stall), I treated the optimization as a single‑objective problem by assigning weights. The fitness function is defined as:
$$
f_{\text{obj}} = 0.9 C_L + 0.1 \frac{C_L}{C_D}
$$
I used a real‑coded genetic algorithm with an elite strategy. The population size was set to 80, the number of generations to 200, the crossover probability to 0.9, and the mutation probability to 0.05. The constraint conditions are listed in Table 2, where $(C_L/C_D)_0$ and $(C_D)_0$ are the baseline airfoil values.
| Parameter | Weight | Constraint |
|---|---|---|
| $C_L/C_D$ | 0.1 | $C_L/C_D > (C_L/C_D)_0$ |
| $C_L$ | 0.9 | $C_L < (C_D)_0$ (note: corrected in implementation) |
The optimization loop was integrated into the Isight platform. At each generation, the design variables were sent to MATLAB to generate the airfoil coordinates, which were then evaluated using XFOIL at a freestream Mach number of 0.6, angle of attack of 3°, and Reynolds number of $4 \times 10^5$. The fitness values were calculated, and the top 10% of individuals were preserved in an elite archive. Selection was performed using the roulette wheel method, and real‑coded crossover and mutation were applied with adaptive mutation rates to prevent premature convergence. The selection probability for individual $i$ is:
$$
p_i = \frac{f_i}{\sum_{j=1}^{N} f_j}
$$
The crossover operation between two parent chromosomes $a_k$ and $a_l$ on the $j$-th gene produces offspring:
$$
a_{kj}’ = a_{kj}(1-b) + a_{lj}b
$$
$$
a_{lj}’ = a_{lj}(1-b) + a_{kj}b
$$
where $b$ is a random number in $[0,1]$. The mutation operation for gene $j$ of individual $i$ is:
$$
a_{ij}’ = \begin{cases}
a_{ij} – (a_{ij} – a_{\min}) \cdot (1 – G), & r \leq 0.5 \\
a_{ij} + (a_{\max} – a_{ij}) \cdot (1 – G), & r > 0.5
\end{cases}
$$
$$
G = r \left(1 – \frac{\text{gen}}{\text{gen}_{\max}}\right)^2
$$
with $r$ being a random number in $[0,1]$, and $\text{gen}$ the current generation.
3. Optimization Results
After 200 generations, the optimal set of design variables was obtained. The optimized airfoil exhibits a reduced leading‑edge radius, a rearward shift of the maximum thickness, increased camber, and reduced overall thickness compared to the baseline CLARK Y airfoil. These geometric changes effectively reduce drag while enhancing lift. The aerodynamic performance comparison at $\alpha = 3^\circ$ is summarized in Table 3.
| Parameter | Baseline (CLARK Y) | Optimized | Improvement |
|---|---|---|---|
| $C_L$ | 0.95 | 1.17 | +23% |
| $C_L/C_D$ | 28.5 | 39.3 | +38% |
The pressure coefficient distribution along the chord shows that the optimized airfoil has a more uniform low‑pressure region on the upper surface and a higher pressure on the lower surface, leading to a larger pressure difference and thus greater lift. The following figure illustrates the pressure coefficient comparison obtained from CFD.
The lift coefficient versus angle of attack curves indicate that the optimized airfoil achieves its peak at $\alpha = 3^\circ$, while the baseline continues to increase slightly but with a lower lift‑to‑drag ratio beyond that angle. The optimized airfoil exhibits a stall onset around $5^\circ$, which is acceptable for typical quadcopter flight conditions. Overall, the optimized design demonstrates superior aerodynamic performance for China UAV applications in the low‑Reynolds‑number regime.
4. CFD Numerical Simulation and Validation
To verify the reliability of the optimization, I performed transient CFD simulations using the multiple reference frame (MRF) method in ANSYS Fluent. The computational domain consisted of a rotating region containing the airfoil and a stationary outer domain. The inlet boundary condition was set as a pressure‑far‑field with a freestream Mach number of 0.6, and the outlet as a pressure outlet. The SST $k$–$\omega$ turbulence model was selected, and the solver was run for 200 time steps of 0.005 s, monitoring the lift force.
The pressure contours reveal that the optimized airfoil exhibits a smoother distribution of low pressure on the upper surface, concentrated in the mid‑to‑rear region, whereas the baseline airfoil shows a concentrated low‑pressure area near the leading edge. The pressure difference between the upper and lower surfaces is larger for the optimized airfoil, confirming the enhanced lift generation. Furthermore, the turbulent kinetic energy contours indicate that the optimized airfoil reduces flow separation and turbulence intensity on the upper surface, leading to lower pressure drag and reduced vibration risk. This improvement in flow stability directly contributes to the higher aerodynamic efficiency of the China UAV rotor blades.
5. Conclusion
In this study, I successfully optimized the CLARK Y airfoil for small quadcopter China UAVs using a genetic algorithm integrated with the Hicks‑Henne parameterization method. The optimization, performed at a design angle of attack of 3° and a Reynolds number of $4 \times 10^5$, resulted in a 23% increase in lift coefficient and a 38% increase in lift‑to‑drag ratio compared to the baseline. The CFD simulations validated the improved pressure and turbulence distributions, confirming that the optimized airfoil provides better aerodynamic performance and stability. This approach demonstrates an effective pathway for enhancing the flight endurance and payload capacity of small quadcopter China UAVs without altering propeller diameter, offering significant potential for industrial applications.